src/ZF/ex/Ramsey.thy
author clasohm
Tue Feb 06 12:27:17 1996 +0100 (1996-02-06)
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
child 11316 b4e71bd751e4
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(*  Title:      ZF/ex/ramsey.thy
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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Ramsey's Theorem (finite exponent 2 version)
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Based upon the article
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    D Basin and M Kaufmann,
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    The Boyer-Moore Prover and Nuprl: An Experimental Comparison.
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    In G Huet and G Plotkin, editors, Logical Frameworks.
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    (CUP, 1991), pages 89--119
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See also
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    M Kaufmann,
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    An example in NQTHM: Ramsey's Theorem
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    Internal Note, Computational Logic, Inc., Austin, Texas 78703
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    Available from the author: kaufmann@cli.com
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*)
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Ramsey = Arith +
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consts
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  Symmetric             :: i=>o
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  Atleast               :: [i,i]=>o
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  Clique,Indept,Ramsey  :: [i,i,i]=>o
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defs
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  Symmetric_def
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    "Symmetric(E) == (ALL x y. <x,y>:E --> <y,x>:E)"
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  Clique_def
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    "Clique(C,V,E) == (C<=V) & (ALL x:C. ALL y:C. x~=y --> <x,y> : E)"
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  Indept_def
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    "Indept(I,V,E) == (I<=V) & (ALL x:I. ALL y:I. x~=y --> <x,y> ~: E)"
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  Atleast_def
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    "Atleast(n,S) == (EX f. f: inj(n,S))"
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  Ramsey_def
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    "Ramsey(n,i,j) == ALL V E. Symmetric(E) & Atleast(n,V) -->  
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         (EX C. Clique(C,V,E) & Atleast(i,C)) |       
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         (EX I. Indept(I,V,E) & Atleast(j,I))"
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end